This invention relates to a cutting machine having a stock suction means and more particularly to a cutting machine having a stock suction means which successively sucks up stock (chip) produced during cutting operations in a machining center with an automatic tool change (ATC) means. In the conventional tool of this type, stock or chip produced during cutting operations are generally left as it is until the machining operation is finished. However, machining with a great amount of stock being remained results in the following problems: Machinability is deteriorated remarkably and the cutting edge of tool is easily worn and damaged; further, the machining accuracy will be reduced if the stock overflows when a workpiece is changed by a pallet changer or if the cut-out chip falls on the reference surface or the like.